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This version indexes the Eulerian numbers in the same way as Graham et al.'s Concrete Mathematics. The traditional indexing, used by Riordan, Comtet and others, is given in A008292, which is the main entry for the Eulerian numbers.

See A131758 for connections of the evaluation of these polynomials at -1 (alternating row sum) to the Euler, Gennochi, Bernoulli, and zag/tangent numbers and values of the Riemann zeta function and polylogarithms. See also A119879 for the Swiss-knife polynomials. - Tom Copeland, Oct 20 2015